LMFDB - Embedded newform 1008.2.ca.c.353.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(257,1008)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1008.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.ca (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.8
Root			$1.71298 + 0.256290i$ of defining polynomial
Character	$\chi$	$=$	1008.353
Dual form			1008.2.ca.c.257.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56012 - 0.752355i) q^{3} +(-1.80966 + 3.13442i) q^{5} +(2.41308 - 1.08492i) q^{7} +(1.86792 - 2.34752i) q^{9} +O(q^{10})$	\(q+(1.56012 - 0.752355i) q^{3} +(-1.80966 + 3.13442i) q^{5} +(2.41308 - 1.08492i) q^{7} +(1.86792 - 2.34752i) q^{9} +(1.73534 - 1.00190i) q^{11} +(2.95206 - 1.70437i) q^{13} +(-0.465079 + 6.25156i) q^{15} +(-3.08709 + 5.34700i) q^{17} +(-0.877353 + 0.506540i) q^{19} +(2.94844 - 3.50809i) q^{21} +(2.62232 + 1.51400i) q^{23} +(-4.04972 - 7.01433i) q^{25} +(1.14800 - 5.06775i) q^{27} +(5.04560 + 2.91308i) q^{29} -0.909687i q^{31} +(1.95354 - 2.86867i) q^{33} +(-0.966257 + 9.52693i) q^{35} +(3.66825 + 6.35359i) q^{37} +(3.32326 - 4.88001i) q^{39} +(-2.85045 - 4.93712i) q^{41} +(2.39949 - 4.15605i) q^{43} +(3.97782 + 10.1031i) q^{45} +2.23022 q^{47} +(4.64590 - 5.23599i) q^{49} +(-0.793376 + 10.6645i) q^{51} +(7.58088 + 4.37683i) q^{53} +7.25237i q^{55} +(-0.987674 + 1.45034i) q^{57} -8.98627 q^{59} +14.7121i q^{61} +(1.96057 - 7.69130i) q^{63} +12.3373i q^{65} +8.31641 q^{67} +(5.23019 + 0.389094i) q^{69} +0.466287i q^{71} +(-3.65022 - 2.10746i) q^{73} +(-11.5953 - 7.89633i) q^{75} +(3.10053 - 4.30036i) q^{77} -3.82533 q^{79} +(-2.02173 - 8.76998i) q^{81} +(4.00481 - 6.93654i) q^{83} +(-11.1732 - 19.3525i) q^{85} +(10.0634 + 0.748656i) q^{87} +(-2.39324 - 4.14521i) q^{89} +(5.27445 - 7.31553i) q^{91} +(-0.684408 - 1.41922i) q^{93} -3.66666i q^{95} +(-10.1835 - 5.87944i) q^{97} +(0.889499 - 5.94521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7}+O(q^{10}) $ 16 * q - 2 * q^7	$ 16 q - 2 q^{7} - 12 q^{11} + 6 q^{13} + 18 q^{15} - 18 q^{17} - 12 q^{21} + 6 q^{23} - 8 q^{25} - 36 q^{27} + 6 q^{29} - 30 q^{35} - 2 q^{37} + 12 q^{39} - 6 q^{41} + 2 q^{43} - 30 q^{45} + 36 q^{47} - 8 q^{49} - 6 q^{51} - 36 q^{53} + 6 q^{57} - 60 q^{59} - 36 q^{63} + 28 q^{67} - 42 q^{69} - 60 q^{75} - 42 q^{77} - 32 q^{79} - 36 q^{81} - 12 q^{85} + 24 q^{87} - 24 q^{89} + 12 q^{91} - 42 q^{93} + 6 q^{97} - 18 q^{99}+O(q^{100}) $ 16 * q - 2 * q^7 - 12 * q^11 + 6 * q^13 + 18 * q^15 - 18 * q^17 - 12 * q^21 + 6 * q^23 - 8 * q^25 - 36 * q^27 + 6 * q^29 - 30 * q^35 - 2 * q^37 + 12 * q^39 - 6 * q^41 + 2 * q^43 - 30 * q^45 + 36 * q^47 - 8 * q^49 - 6 * q^51 - 36 * q^53 + 6 * q^57 - 60 * q^59 - 36 * q^63 + 28 * q^67 - 42 * q^69 - 60 * q^75 - 42 * q^77 - 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^87 - 24 * q^89 + 12 * q^91 - 42 * q^93 + 6 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.56012	−	0.752355i	0.900733	−	0.434373i
$3$	1.56012	−	0.752355i	0.900733	−	0.434373i
$4$		0			0
$5$	−1.80966	+	3.13442i	−0.809304	+	1.40175i	0.104043	+	0.994573i	$0.466822\pi$
$5$	−1.80966	+	3.13442i	−0.809304	+	1.40175i	−0.913347	+	0.407182i	$0.866511\pi$
$6$		0			0
$7$	2.41308	−	1.08492i	0.912058	−	0.410061i
$7$	2.41308	−	1.08492i	0.912058	−	0.410061i
$8$		0			0
$9$	1.86792	−	2.34752i	0.622641	−	0.782508i
$10$		0			0
$11$	1.73534	−	1.00190i	0.523224	−	0.302083i	−0.215029	−	0.976608i	$-0.568985\pi$
$11$	1.73534	−	1.00190i	0.523224	−	0.302083i	0.738253	+	0.674524i	$0.235651\pi$
$12$		0			0
$13$	2.95206	−	1.70437i	0.818754	−	0.472708i	−0.0312328	−	0.999512i	$-0.509943\pi$
$13$	2.95206	−	1.70437i	0.818754	−	0.472708i	0.849987	+	0.526804i	$0.176610\pi$
$14$		0			0
$15$	−0.465079	+	6.25156i	−0.120083	+	1.61415i
$16$		0			0
$17$	−3.08709	+	5.34700i	−0.748730	+	1.29684i	0.199702	+	0.979857i	$0.436002\pi$
$17$	−3.08709	+	5.34700i	−0.748730	+	1.29684i	−0.948432	+	0.316981i	$0.897331\pi$
$18$		0			0
$19$	−0.877353	+	0.506540i	−0.201279	+	0.116208i	−0.597252	−	0.802054i	$-0.703741\pi$
$19$	−0.877353	+	0.506540i	−0.201279	+	0.116208i	0.395973	+	0.918262i	$0.370407\pi$
$20$		0			0
$21$	2.94844	−	3.50809i	0.643402	−	0.765528i
$22$		0			0
$23$	2.62232	+	1.51400i	0.546791	+	0.315690i	0.747827	−	0.663894i	$-0.231097\pi$
$23$	2.62232	+	1.51400i	0.546791	+	0.315690i	−0.201035	+	0.979584i	$0.564431\pi$
$24$		0			0
$25$	−4.04972	−	7.01433i	−0.809945	−	1.40287i
$26$		0			0
$27$	1.14800	−	5.06775i	0.220934	−	0.975289i
$28$		0			0
$29$	5.04560	+	2.91308i	0.936945	+	0.540945i	0.889001	−	0.457905i	$-0.151400\pi$
$29$	5.04560	+	2.91308i	0.936945	+	0.540945i	0.0479434	+	0.998850i	$0.484733\pi$
$30$		0			0
$31$		−	0.909687i		−	0.163385i	−0.996658	−	0.0816923i	$-0.973968\pi$
$31$		−	0.909687i		−	0.163385i	0.996658	−	0.0816923i	$-0.0260325\pi$
$32$		0			0
$33$	1.95354	−	2.86867i	0.340068	−	0.499371i
$34$		0			0
$35$	−0.966257	+	9.52693i	−0.163327	+	1.61035i
$36$		0			0
$37$	3.66825	+	6.35359i	0.603056	+	1.04452i	0.992355	+	0.123413i	$0.0393839\pi$
$37$	3.66825	+	6.35359i	0.603056	+	1.04452i	−0.389299	+	0.921111i	$0.627283\pi$
$38$		0			0
$39$	3.32326	−	4.88001i	0.532148	−	0.781428i
$40$		0			0
$41$	−2.85045	−	4.93712i	−0.445165	−	0.771048i	0.552899	−	0.833248i	$-0.313522\pi$
$41$	−2.85045	−	4.93712i	−0.445165	−	0.771048i	−0.998064	+	0.0622002i	$0.980188\pi$
$42$		0			0
$43$	2.39949	−	4.15605i	0.365919	−	0.633791i	−0.623004	−	0.782219i	$-0.714088\pi$
$43$	2.39949	−	4.15605i	0.365919	−	0.633791i	0.988923	+	0.148428i	$0.0474212\pi$
$44$		0			0
$45$	3.97782	+	10.1031i	0.592978	+	1.50608i
$46$		0			0
$47$	2.23022			0.325311			0.162655	−	0.986683i	$-0.447994\pi$
$47$	2.23022			0.325311			0.162655	+	0.986683i	$0.447994\pi$
$48$		0			0
$49$	4.64590	−	5.23599i	0.663700	−	0.747999i
$50$		0			0
$51$	−0.793376	+	10.6645i	−0.111095	+	1.49333i
$52$		0			0
$53$	7.58088	+	4.37683i	1.04131	+	0.601203i	0.920205	−	0.391436i	$-0.128022\pi$
$53$	7.58088	+	4.37683i	1.04131	+	0.601203i	0.121109	+	0.992639i	$0.461355\pi$
$54$		0			0
$55$			7.25237i			0.977909i
$56$		0			0
$57$	−0.987674	+	1.45034i	−0.130821	+	0.192103i
$58$		0			0
$59$	−8.98627			−1.16991			−0.584956	−	0.811065i	$-0.698888\pi$
$59$	−8.98627			−1.16991			−0.584956	+	0.811065i	$0.698888\pi$
$60$		0			0
$61$			14.7121i			1.88369i	0.336053	+	0.941843i	$0.390908\pi$
$61$			14.7121i			1.88369i	−0.336053	+	0.941843i	$0.609092\pi$
$62$		0			0
$63$	1.96057	−	7.69130i	0.247009	−	0.969013i
$64$		0			0
$65$			12.3373i			1.53026i
$66$		0			0
$67$	8.31641			1.01601			0.508006	−	0.861354i	$-0.330383\pi$
$67$	8.31641			1.01601			0.508006	+	0.861354i	$0.330383\pi$
$68$		0			0
$69$	5.23019	+	0.389094i	0.629640	+	0.0468415i
$70$		0			0
$71$			0.466287i			0.0553381i	0.999617	+	0.0276691i	$0.00880846\pi$
$71$			0.466287i			0.0553381i	−0.999617	+	0.0276691i	$0.991192\pi$
$72$		0			0
$73$	−3.65022	−	2.10746i	−0.427226	−	0.246659i	0.270938	−	0.962597i	$-0.412666\pi$
$73$	−3.65022	−	2.10746i	−0.427226	−	0.246659i	−0.698164	+	0.715938i	$0.746000\pi$
$74$		0			0
$75$	−11.5953	−	7.89633i	−1.33891	−	0.911790i
$76$		0			0
$77$	3.10053	−	4.30036i	0.353338	−	0.490071i
$78$		0			0
$79$	−3.82533			−0.430384			−0.215192	−	0.976572i	$-0.569038\pi$
$79$	−3.82533			−0.430384			−0.215192	+	0.976572i	$0.569038\pi$
$80$		0			0
$81$	−2.02173	−	8.76998i	−0.224637	−	0.974443i
$82$		0			0
$83$	4.00481	−	6.93654i	0.439585	−	0.761384i	−0.558072	−	0.829792i	$-0.688459\pi$
$83$	4.00481	−	6.93654i	0.439585	−	0.761384i	0.997657	+	0.0684084i	$0.0217921\pi$
$84$		0			0
$85$	−11.1732	−	19.3525i	−1.21190	−	2.09907i
$86$		0			0
$87$	10.0634	+	0.748656i	1.07891	+	0.0802643i
$88$		0			0
$89$	−2.39324	−	4.14521i	−0.253683	−	0.439391i	0.710854	−	0.703339i	$-0.248309\pi$
$89$	−2.39324	−	4.14521i	−0.253683	−	0.439391i	−0.964537	+	0.263948i	$0.914975\pi$
$90$		0			0
$91$	5.27445	−	7.31553i	0.552912	−	0.766876i
$92$		0			0
$93$	−0.684408	−	1.41922i	−0.0709698	−	0.147166i
$94$		0			0
$95$		−	3.66666i		−	0.376191i
$96$		0			0
$97$	−10.1835	−	5.87944i	−1.03398	−	0.596967i	−0.115856	−	0.993266i	$-0.536961\pi$
$97$	−10.1835	−	5.87944i	−1.03398	−	0.596967i	−0.918121	+	0.396299i	$0.870294\pi$
$98$		0			0
$99$	0.889499	−	5.94521i	0.0893980	−	0.597516i
$100$		0			0
$101$	−6.44610	−	11.1650i	−0.641411	−	1.11096i	−0.985118	−	0.171879i	$-0.945016\pi$
$101$	−6.44610	−	11.1650i	−0.641411	−	1.11096i	0.343707	−	0.939077i	$-0.388317\pi$
$102$		0			0
$103$	−9.31740	−	5.37940i	−0.918070	−	0.530048i	−0.0350515	−	0.999386i	$-0.511160\pi$
$103$	−9.31740	−	5.37940i	−0.918070	−	0.530048i	−0.883019	+	0.469337i	$0.844493\pi$
$104$		0			0
$105$	5.66017	+	15.5901i	0.552376	+	1.52144i
$106$		0			0
$107$	2.28602	−	1.31983i	0.220998	−	0.127593i	−0.385414	−	0.922744i	$-0.625942\pi$
$107$	2.28602	−	1.31983i	0.220998	−	0.127593i	0.606412	+	0.795151i	$0.292608\pi$
$108$		0			0
$109$	4.51768	−	7.82484i	0.432715	−	0.749484i	−0.564391	−	0.825507i	$-0.690889\pi$
$109$	4.51768	−	7.82484i	0.432715	−	0.749484i	0.997106	+	0.0760233i	$0.0242224\pi$
$110$		0			0
$111$	10.5031	+	7.15251i	0.996905	+	0.678886i
$112$		0			0
$113$	−1.46411	+	0.845306i	−0.137732	+	0.0795197i	−0.567283	−	0.823523i	$-0.692005\pi$
$113$	−1.46411	+	0.845306i	−0.137732	+	0.0795197i	0.429551	+	0.903043i	$0.358672\pi$
$114$		0			0
$115$	−9.49100	+	5.47963i	−0.885041	+	0.510978i
$116$		0			0
$117$	1.51317	−	10.1137i	0.139892	−	0.935008i
$118$		0			0
$119$	−1.64833	+	16.2520i	−0.151103	+	1.48982i
$120$		0			0
$121$	−3.49240	+	6.04902i	−0.317491	+	0.549911i
$122$		0			0
$123$	−8.16149	−	5.55793i	−0.735897	−	0.501141i
$124$		0			0
$125$	11.2179			1.00336
$126$		0			0
$127$	−17.9292			−1.59096			−0.795478	−	0.605983i	$-0.792780\pi$
$127$	−17.9292			−1.59096			−0.795478	+	0.605983i	$0.792780\pi$
$128$		0			0
$129$	0.616665	−	8.28919i	0.0542944	−	0.729822i
$130$		0			0
$131$	−8.66567	+	15.0094i	−0.757123	+	1.31138i	0.187188	+	0.982324i	$0.440062\pi$
$131$	−8.66567	+	15.0094i	−0.757123	+	1.31138i	−0.944312	+	0.329052i	$0.893271\pi$
$132$		0			0
$133$	−1.56757	+	2.17418i	−0.135925	+	0.188525i
$134$		0			0
$135$	13.8070	+	12.7692i	1.18831	+	1.09900i
$136$		0			0
$137$	0.000558693	0	0.000322562i	4.77324e−5	0	2.75583e-5i	−0.499976	−	0.866039i	$-0.666658\pi$
$137$	0.000558693	0	0.000322562i	4.77324e−5	0	2.75583e-5i	0.500024	+	0.866012i	$0.333325\pi$
$138$		0			0
$139$	8.73273	−	5.04185i	0.740701	−	0.427644i	−0.0816233	−	0.996663i	$-0.526010\pi$
$139$	8.73273	−	5.04185i	0.740701	−	0.427644i	0.822324	+	0.569019i	$0.192677\pi$
$140$		0			0
$141$	3.47940	−	1.67792i	0.293018	−	0.141306i
$142$		0			0
$143$	3.41521	−	5.91532i	0.285594	−	0.494664i
$144$		0			0
$145$	−18.2616	+	10.5434i	−1.51655	+	0.875578i
$146$		0			0
$147$	3.30882	−	11.6641i	0.272907	−	0.962040i
$148$		0			0
$149$	−9.74064	−	5.62376i	−0.797984	−	0.460716i	0.0447816	−	0.998997i	$-0.485741\pi$
$149$	−9.74064	−	5.62376i	−0.797984	−	0.460716i	−0.842766	+	0.538280i	$0.819074\pi$
$150$		0			0
$151$	−2.36189	−	4.09092i	−0.192208	−	0.332914i	0.753774	−	0.657134i	$-0.228232\pi$
$151$	−2.36189	−	4.09092i	−0.192208	−	0.332914i	−0.945982	+	0.324220i	$0.894898\pi$
$152$		0			0
$153$	6.78575	+	17.2348i	0.548596	+	1.39335i
$154$		0			0
$155$	2.85134	+	1.64622i	0.229025	+	0.132228i
$156$		0			0
$157$			3.06972i			0.244990i	0.992469	+	0.122495i	$0.0390895\pi$
$157$			3.06972i			0.244990i	−0.992469	+	0.122495i	$0.960910\pi$
$158$		0			0
$159$	15.1200	+	1.12484i	1.19909	+	0.0892053i
$160$		0			0
$161$	7.97043	+	0.808390i	0.628158	+	0.0637101i
$162$		0			0
$163$	1.43687	+	2.48873i	0.112544	+	0.194932i	0.916795	−	0.399357i	$-0.130767\pi$
$163$	1.43687	+	2.48873i	0.112544	+	0.194932i	−0.804251	+	0.594289i	$0.797433\pi$
$164$		0			0
$165$	5.45636	+	11.3145i	0.424777	+	0.880835i
$166$		0			0
$167$	−0.730517	−	1.26529i	−0.0565291	−	0.0979113i	0.836376	−	0.548156i	$-0.184670\pi$
$167$	−0.730517	−	1.26529i	−0.0565291	−	0.0979113i	−0.892905	+	0.450245i	$0.851337\pi$
$168$		0			0
$169$	−0.690233	+	1.19552i	−0.0530948	+	0.0919630i
$170$		0			0
$171$	−0.449713	+	3.00578i	−0.0343904	+	0.229858i
$172$		0			0
$173$	−3.07081			−0.233470			−0.116735	−	0.993163i	$-0.537243\pi$
$173$	−3.07081			−0.233470			−0.116735	+	0.993163i	$0.537243\pi$
$174$		0			0
$175$	−17.3823	−	12.5325i	−1.31398	−	0.947368i
$176$		0			0
$177$	−14.0196	+	6.76087i	−1.05378	+	0.508178i
$178$		0			0
$179$	−16.7310	−	9.65966i	−1.25054	−	0.721997i	−0.279320	−	0.960198i	$-0.590109\pi$
$179$	−16.7310	−	9.65966i	−1.25054	−	0.721997i	−0.971216	+	0.238201i	$0.923442\pi$
$180$		0			0
$181$			7.89318i			0.586695i	0.956006	+	0.293348i	$0.0947693\pi$
$181$			7.89318i			0.586695i	−0.956006	+	0.293348i	$0.905231\pi$
$182$		0			0
$183$	11.0687	+	22.9525i	0.818222	+	1.69670i
$184$		0			0
$185$	−26.5531			−1.95222
$186$		0			0
$187$			12.3718i			0.904715i
$188$		0			0
$189$	−2.72787	−	13.4744i	−0.198424	−	0.980116i
$190$		0			0
$191$		−	13.3042i		−	0.962660i	−0.876540	−	0.481330i	$-0.840154\pi$
$191$		−	13.3042i		−	0.962660i	0.876540	−	0.481330i	$-0.159846\pi$
$192$		0			0
$193$	6.53573			0.470452			0.235226	−	0.971941i	$-0.424417\pi$
$193$	6.53573			0.470452			0.235226	+	0.971941i	$0.424417\pi$
$194$		0			0
$195$	9.28205	+	19.2476i	0.664701	+	1.37835i
$196$		0			0
$197$			4.44250i			0.316515i	0.987398	+	0.158258i	$0.0505876\pi$
$197$			4.44250i			0.316515i	−0.987398	+	0.158258i	$0.949412\pi$
$198$		0			0
$199$	−9.96868	−	5.75542i	−0.706661	−	0.407991i	0.103163	−	0.994665i	$-0.467104\pi$
$199$	−9.96868	−	5.75542i	−0.706661	−	0.407991i	−0.809823	+	0.586674i	$0.800437\pi$
$200$		0			0
$201$	12.9746	−	6.25690i	0.915155	−	0.441328i
$202$		0			0
$203$	15.3359	+	1.55542i	1.07637	+	0.109169i
$204$		0			0
$205$	20.6333			1.44109
$206$		0			0
$207$	8.45243	−	3.32793i	0.587485	−	0.231307i
$208$		0			0
$209$	−1.01500	+	1.75804i	−0.0702092	+	0.121606i
$210$		0			0
$211$	−11.3005	−	19.5731i	−0.777961	−	1.34747i	−0.933115	−	0.359577i	$-0.882921\pi$
$211$	−11.3005	−	19.5731i	−0.777961	−	1.34747i	0.155155	−	0.987890i	$-0.450412\pi$
$212$		0			0
$213$	0.350814	+	0.727462i	0.0240374	+	0.0498449i
$214$		0			0
$215$	8.68453	+	15.0420i	0.592280	+	1.02586i
$216$		0			0
$217$	−0.986937	−	2.19515i	−0.0669976	−	0.149016i
$218$		0			0
$219$	−7.28033	−	0.541613i	−0.491959	−	0.0365988i
$220$		0			0
$221$			21.0462i			1.41572i
$222$		0			0
$223$	−16.2994	−	9.41045i	−1.09149	−	0.630170i	−0.157515	−	0.987517i	$-0.550348\pi$
$223$	−16.2994	−	9.41045i	−1.09149	−	0.630170i	−0.933972	+	0.357346i	$0.883682\pi$
$224$		0			0
$225$	−24.0309	−	3.59540i	−1.60206	−	0.239693i
$226$		0			0
$227$	7.30665	+	12.6555i	0.484960	+	0.839975i	0.999851	−	0.0172809i	$-0.00550095\pi$
$227$	7.30665	+	12.6555i	0.484960	+	0.839975i	−0.514891	+	0.857256i	$0.672168\pi$
$228$		0			0
$229$	2.06044	+	1.18959i	0.136158	+	0.0786106i	0.566531	−	0.824040i	$-0.308285\pi$
$229$	2.06044	+	1.18959i	0.136158	+	0.0786106i	−0.430374	+	0.902651i	$0.641618\pi$
$230$		0			0
$231$	1.60179	−	9.04176i	0.105390	−	0.594904i
$232$		0			0
$233$	9.03470	−	5.21619i	0.591883	−	0.341724i	−0.173959	−	0.984753i	$-0.555656\pi$
$233$	9.03470	−	5.21619i	0.591883	−	0.341724i	0.765842	+	0.643029i	$0.222323\pi$
$234$		0			0
$235$	−4.03593	+	6.99044i	−0.263275	+	0.456006i
$236$		0			0
$237$	−5.96796	+	2.87801i	−0.387661	+	0.186947i
$238$		0			0
$239$	−20.5971	+	11.8917i	−1.33232	+	0.769213i	−0.985654	−	0.168777i	$-0.946018\pi$
$239$	−20.5971	+	11.8917i	−1.33232	+	0.769213i	−0.346662	+	0.937990i	$0.612685\pi$
$240$		0			0
$241$	24.8105	−	14.3243i	1.59818	−	0.922712i	0.606348	−	0.795200i	$-0.292634\pi$
$241$	24.8105	−	14.3243i	1.59818	−	0.922712i	0.991837	−	0.127513i	$-0.0406994\pi$
$242$		0			0
$243$	−9.75228	−	12.1611i	−0.625609	−	0.780137i
$244$		0			0
$245$	8.00430	+	24.0376i	0.511376	+	1.53570i
$246$		0			0
$247$	−1.72667	+	2.99067i	−0.109865	+	0.190292i
$248$		0			0
$249$	1.02923	−	13.8348i	0.0652248	−	0.876748i
$250$		0			0
$251$	11.0301			0.696216			0.348108	−	0.937454i	$-0.386824\pi$
$251$	11.0301			0.696216			0.348108	+	0.937454i	$0.386824\pi$
$252$		0			0
$253$	6.06748			0.381459
$254$		0			0
$255$	−31.9914	−	21.7859i	−2.00338	−	1.36429i
$256$		0			0
$257$	−7.54890	+	13.0751i	−0.470888	+	0.815601i	−0.999446	−	0.0332960i	$-0.989400\pi$
$257$	−7.54890	+	13.0751i	−0.470888	+	0.815601i	0.528558	+	0.848897i	$0.322733\pi$
$258$		0			0
$259$	15.7449	+	11.3520i	0.978341	+	0.705377i
$260$		0			0
$261$	16.2633	−	6.40326i	1.00667	−	0.396352i
$262$		0			0
$263$	−17.0075	+	9.81926i	−1.04873	+	0.605482i	−0.922292	−	0.386493i	$-0.873686\pi$
$263$	−17.0075	+	9.81926i	−1.04873	+	0.605482i	−0.126433	+	0.991975i	$0.540353\pi$
$264$		0			0
$265$	−27.4376	+	15.8411i	−1.68548	+	0.973112i
$266$		0			0
$267$	−6.85240	−	4.66644i	−0.419360	−	0.285581i
$268$		0			0
$269$	0.245503	−	0.425223i	0.0149686	−	0.0259263i	−0.858444	−	0.512907i	$-0.828569\pi$
$269$	0.245503	−	0.425223i	0.0149686	−	0.0259263i	0.873413	+	0.486981i	$0.161902\pi$
$270$		0			0
$271$	12.1927	−	7.03945i	0.740653	−	0.427616i	−0.0816537	−	0.996661i	$-0.526020\pi$
$271$	12.1927	−	7.03945i	0.740653	−	0.427616i	0.822307	+	0.569045i	$0.192687\pi$
$272$		0			0
$273$	2.72487	−	15.3813i	0.164917	−	0.930920i
$274$		0			0
$275$	−14.0553	−	8.11481i	−0.847565	−	0.489342i
$276$		0			0
$277$	−15.3600	−	26.6043i	−0.922894	−	1.59850i	−0.794913	−	0.606723i	$-0.792484\pi$
$277$	−15.3600	−	26.6043i	−0.922894	−	1.59850i	−0.127981	−	0.991777i	$-0.540850\pi$
$278$		0			0
$279$	−2.13551	−	1.69923i	−0.127850	−	0.101730i
$280$		0			0
$281$	6.86286	+	3.96227i	0.409404	+	0.236369i	0.690534	−	0.723300i	$-0.257376\pi$
$281$	6.86286	+	3.96227i	0.409404	+	0.236369i	−0.281130	+	0.959670i	$0.590709\pi$
$282$		0			0
$283$			11.5159i			0.684547i	0.939600	+	0.342273i	$0.111197\pi$
$283$			11.5159i			0.684547i	−0.939600	+	0.342273i	$0.888803\pi$
$284$		0			0
$285$	−2.75863	−	5.72041i	−0.163407	−	0.338848i
$286$		0			0
$287$	−12.2347	−	8.82115i	−0.722193	−	0.520696i
$288$		0			0
$289$	−10.5603	−	18.2909i	−0.621192	−	1.07594i
$290$		0			0
$291$	−20.3109	−	1.51101i	−1.19064	−	0.0885767i
$292$		0			0
$293$	−2.50937	−	4.34636i	−0.146599	−	0.253917i	0.783369	−	0.621557i	$-0.213499\pi$
$293$	−2.50937	−	4.34636i	−0.146599	−	0.253917i	−0.929968	+	0.367639i	$0.880166\pi$
$294$		0			0
$295$	16.2621	−	28.1667i	0.946814	−	1.63993i
$296$		0			0
$297$	−3.08519	−	9.94444i	−0.179021	−	0.577035i
$298$		0			0
$299$	10.3217			0.596917
$300$		0			0
$301$	1.28120	−	12.6321i	0.0738469	−	0.728104i
$302$		0			0
$303$	−18.4567	−	12.5689i	−1.06031	−	0.722064i
$304$		0			0
$305$	−46.1138	−	26.6238i	−2.64047	−	1.52447i
$306$		0			0
$307$			17.5309i			1.00054i	0.865869	+	0.500271i	$0.166766\pi$
$307$			17.5309i			1.00054i	−0.865869	+	0.500271i	$0.833234\pi$
$308$		0			0
$309$	−18.5834	−	1.38250i	−1.05717	−	0.0786474i
$310$		0			0
$311$	−17.2952			−0.980720			−0.490360	−	0.871520i	$-0.663135\pi$
$311$	−17.2952			−0.980720			−0.490360	+	0.871520i	$0.663135\pi$
$312$		0			0
$313$		−	8.99498i		−	0.508426i	−0.967148	−	0.254213i	$-0.918184\pi$
$313$		−	8.99498i		−	0.508426i	0.967148	−	0.254213i	$-0.0818165\pi$
$314$		0			0
$315$	20.5598	+	20.0639i	1.15841	+	1.13047i
$316$		0			0
$317$		−	6.72038i		−	0.377454i	−0.982030	−	0.188727i	$-0.939564\pi$
$317$		−	6.72038i		−	0.377454i	0.982030	−	0.188727i	$-0.0604362\pi$
$318$		0			0
$319$	11.6744			0.653642
$320$		0			0
$321$	2.57347	−	3.77899i	0.143637	−	0.210923i
$322$		0			0
$323$		−	6.25494i		−	0.348034i
$324$		0			0
$325$	−23.9100	−	13.8045i	−1.32629	−	0.765734i
$326$		0			0
$327$	1.16103	−	15.6066i	0.0642053	−	0.863045i
$328$		0			0
$329$	5.38169	−	2.41961i	0.296702	−	0.133397i
$330$		0			0
$331$	18.7745			1.03194			0.515970	−	0.856607i	$-0.327432\pi$
$331$	18.7745			1.03194			0.515970	+	0.856607i	$0.327432\pi$
$332$		0			0
$333$	21.7672	+	3.25672i	1.19284	+	0.178467i
$334$		0			0
$335$	−15.0499	+	26.0671i	−0.822262	+	1.42420i
$336$		0			0
$337$	2.42287	+	4.19654i	0.131982	+	0.228600i	0.924441	−	0.381326i	$-0.124532\pi$
$337$	2.42287	+	4.19654i	0.131982	+	0.228600i	−0.792458	+	0.609926i	$0.791199\pi$
$338$		0			0
$339$	−1.64822	+	2.42031i	−0.0895188	+	0.131453i
$340$		0			0
$341$	−0.911413	−	1.57861i	−0.0493558	−	0.0854868i
$342$		0			0
$343$	5.53030	−	17.6753i	0.298608	−	0.954376i
$344$		0			0
$345$	−10.6844	+	15.6895i	−0.575230	+	0.844693i
$346$		0			0
$347$		−	17.4712i		−	0.937902i	−0.883224	−	0.468951i	$-0.844632\pi$
$347$		−	17.4712i		−	0.937902i	0.883224	−	0.468951i	$-0.155368\pi$
$348$		0			0
$349$	20.6338	+	11.9129i	1.10450	+	0.637683i	0.937399	−	0.348257i	$-0.113226\pi$
$349$	20.6338	+	11.9129i	1.10450	+	0.637683i	0.167101	+	0.985940i	$0.446560\pi$
$350$		0			0
$351$	−5.24835	−	16.9169i	−0.280136	−	0.902958i
$352$		0			0
$353$	5.02061	+	8.69596i	0.267220	+	0.462839i	0.968143	−	0.250398i	$-0.0805615\pi$
$353$	5.02061	+	8.69596i	0.267220	+	0.462839i	−0.700923	+	0.713237i	$0.747228\pi$
$354$		0			0
$355$	−1.46154	−	0.843820i	−0.0775705	−	0.0447853i
$356$		0			0
$357$	9.65567	+	26.5951i	0.511032	+	1.40756i
$358$		0			0
$359$	10.5353	−	6.08254i	0.556030	−	0.321024i	−0.195521	−	0.980700i	$-0.562640\pi$
$359$	10.5353	−	6.08254i	0.556030	−	0.321024i	0.751550	+	0.659676i	$0.229306\pi$
$360$		0			0
$361$	−8.98683	+	15.5657i	−0.472991	+	0.819245i
$362$		0			0
$363$	−0.897541	+	12.0647i	−0.0471087	+	0.633233i
$364$		0			0
$365$	13.2113	−	7.62756i	0.691512	−	0.399245i
$366$		0			0
$367$	−3.14420	+	1.81531i	−0.164126	+	0.0947582i	−0.579813	−	0.814749i	$-0.696874\pi$
$367$	−3.14420	+	1.81531i	−0.164126	+	0.0947582i	0.415687	+	0.909508i	$0.363541\pi$
$368$		0			0
$369$	−16.9144	−	2.53067i	−0.880529	−	0.131741i
$370$		0			0
$371$	23.0418	+	2.33698i	1.19627	+	0.121330i
$372$		0			0
$373$	−2.74616	+	4.75648i	−0.142191	+	0.246281i	−0.928321	−	0.371779i	$-0.878748\pi$
$373$	−2.74616	+	4.75648i	−0.142191	+	0.246281i	0.786131	+	0.618060i	$0.212081\pi$
$374$		0			0
$375$	17.5012	−	8.43983i	0.903757	−	0.435831i
$376$		0			0
$377$	19.8599			1.02284
$378$		0			0
$379$	15.5960			0.801112			0.400556	−	0.916272i	$-0.368817\pi$
$379$	15.5960			0.801112			0.400556	+	0.916272i	$0.368817\pi$
$380$		0			0
$381$	−27.9716	+	13.4891i	−1.43303	+	0.691067i
$382$		0			0
$383$	−4.71534	+	8.16720i	−0.240942	+	0.417324i	−0.960983	−	0.276607i	$-0.910790\pi$
$383$	−4.71534	+	8.16720i	−0.240942	+	0.417324i	0.720041	+	0.693932i	$0.244123\pi$
$384$		0			0
$385$	7.86823	+	17.5005i	0.401002	+	0.891910i
$386$		0			0
$387$	−5.27434	−	13.3960i	−0.268110	−	0.680959i
$388$		0			0
$389$	5.56142	−	3.21089i	0.281975	−	0.162798i	−0.352342	−	0.935871i	$-0.614615\pi$
$389$	5.56142	−	3.21089i	0.281975	−	0.162798i	0.634317	+	0.773073i	$0.281281\pi$
$390$		0			0
$391$	−16.1907	+	9.34769i	−0.818798	+	0.472733i
$392$		0			0
$393$	−2.22706	+	29.9360i	−0.112340	+	1.51007i
$394$		0			0
$395$	6.92255	−	11.9902i	0.348311	−	0.603293i
$396$		0			0
$397$	5.99750	−	3.46266i	0.301006	−	0.173786i	−0.341889	−	0.939740i	$-0.611067\pi$
$397$	5.99750	−	3.46266i	0.301006	−	0.173786i	0.642895	+	0.765955i	$0.277733\pi$
$398$		0			0
$399$	−0.809832	+	4.57134i	−0.0405423	+	0.228853i
$400$		0			0
$401$	−9.16848	−	5.29343i	−0.457852	−	0.264341i	0.253289	−	0.967391i	$-0.418488\pi$
$401$	−9.16848	−	5.29343i	−0.457852	−	0.264341i	−0.711141	+	0.703050i	$0.751821\pi$
$402$		0			0
$403$	−1.55045	−	2.68545i	−0.0772332	−	0.133772i
$404$		0			0
$405$	31.1474	+	9.53372i	1.54773	+	0.473735i
$406$		0			0
$407$	12.7313	+	7.35042i	0.631067	+	0.364347i
$408$		0			0
$409$			8.92343i			0.441235i	0.975360	+	0.220618i	$0.0708073\pi$
$409$			8.92343i			0.441235i	−0.975360	+	0.220618i	$0.929193\pi$
$410$		0			0
$411$	0.000628945	0	0.000923569i	3.10236e−5	0	4.55563e-5i
$412$		0			0
$413$	−21.6846	+	9.74937i	−1.06703	+	0.479735i
$414$		0			0
$415$	14.4947	+	25.1055i	0.711516	+	1.23238i
$416$		0			0
$417$	9.83082	−	14.4360i	0.481417	−	0.706933i
$418$		0			0
$419$	−17.1924	−	29.7781i	−0.839903	−	1.45475i	−0.889975	−	0.456009i	$-0.849279\pi$
$419$	−17.1924	−	29.7781i	−0.839903	−	1.45475i	0.0500724	−	0.998746i	$-0.484055\pi$
$420$		0			0
$421$	−17.7840	+	30.8028i	−0.866739	+	1.50124i	−0.00142877	+	0.999999i	$0.500455\pi$
$421$	−17.7840	+	30.8028i	−0.866739	+	1.50124i	−0.865310	+	0.501237i	$0.832879\pi$
$422$		0			0
$423$	4.16587	−	5.23549i	0.202552	−	0.254558i
$424$		0			0
$425$	50.0075			2.42572
$426$		0			0
$427$	15.9614	+	35.5014i	0.772426	+	1.71803i
$428$		0			0
$429$	0.877703	−	11.7980i	0.0423759	−	0.569615i
$430$		0			0
$431$	26.7338	+	15.4348i	1.28772	+	0.743466i	0.978247	−	0.207442i	$-0.0665138\pi$
$431$	26.7338	+	15.4348i	1.28772	+	0.743466i	0.309474	+	0.950908i	$0.399847\pi$
$432$		0			0
$433$		−	23.2463i		−	1.11715i	−0.829455	−	0.558574i	$-0.811349\pi$
$433$		−	23.2463i		−	1.11715i	0.829455	−	0.558574i	$-0.188651\pi$
$434$		0			0
$435$	−20.5579	+	30.1881i	−0.985676	+	1.44741i
$436$		0			0
$437$	−3.06760			−0.146743
$438$		0			0
$439$			22.2727i			1.06302i	0.847052	+	0.531509i	$0.178375\pi$
$439$			22.2727i			1.06302i	−0.847052	+	0.531509i	$0.821625\pi$
$440$		0			0
$441$	−3.61342	−	20.6868i	−0.172068	−	0.985085i
$442$		0			0
$443$		−	17.9852i		−	0.854501i	−0.904133	−	0.427251i	$-0.859482\pi$
$443$		−	17.9852i		−	0.854501i	0.904133	−	0.427251i	$-0.140518\pi$
$444$		0			0
$445$	17.3238			0.821225
$446$		0			0
$447$	−19.4276	−	1.44530i	−0.918894	−	0.0683601i
$448$		0			0
$449$		−	9.44363i		−	0.445673i	−0.974856	−	0.222836i	$-0.928468\pi$
$449$		−	9.44363i		−	0.445673i	0.974856	−	0.222836i	$-0.0715315\pi$
$450$		0			0
$451$	−9.89297	−	5.71171i	−0.465842	−	0.268954i
$452$		0			0
$453$	−6.76266	−	4.60533i	−0.317737	−	0.216377i
$454$		0			0
$455$	13.3850	+	29.7709i	0.627498	+	1.39568i
$456$		0			0
$457$	−1.84450			−0.0862821			−0.0431411	−	0.999069i	$-0.513736\pi$
$457$	−1.84450			−0.0862821			−0.0431411	+	0.999069i	$0.513736\pi$
$458$		0			0
$459$	23.5533	+	21.7830i	1.09937	+	1.01674i
$460$		0			0
$461$	−18.1869	+	31.5007i	−0.847050	+	1.46713i	0.0367790	+	0.999323i	$0.488290\pi$
$461$	−18.1869	+	31.5007i	−0.847050	+	1.46713i	−0.883829	+	0.467810i	$0.845043\pi$
$462$		0			0
$463$	15.9830	+	27.6834i	0.742794	+	1.28656i	0.951219	+	0.308518i	$0.0998330\pi$
$463$	15.9830	+	27.6834i	0.742794	+	1.28656i	−0.208425	+	0.978038i	$0.566834\pi$
$464$		0			0
$465$	5.68697	+	0.423076i	0.263727	+	0.0196197i
$466$		0			0
$467$	−12.2206	−	21.1666i	−0.565500	−	0.979475i	−0.997003	−	0.0773632i	$-0.975350\pi$
$467$	−12.2206	−	21.1666i	−0.565500	−	0.979475i	0.431503	−	0.902112i	$-0.357983\pi$
$468$		0			0
$469$	20.0682	−	9.02263i	0.926662	−	0.416627i
$470$		0			0
$471$	2.30952	+	4.78911i	0.106417	+	0.220671i
$472$		0			0
$473$		−	9.61619i		−	0.442153i
$474$		0			0
$475$	7.10607	+	4.10269i	0.326049	+	0.188245i
$476$		0			0
$477$	24.4352	−	9.62073i	1.11881	−	0.440503i
$478$		0			0
$479$	−5.48032	−	9.49220i	−0.250402	−	0.433710i	0.713234	−	0.700926i	$-0.247230\pi$
$479$	−5.48032	−	9.49220i	−0.250402	−	0.433710i	−0.963637	+	0.267216i	$0.913896\pi$
$480$		0			0
$481$	21.6578	+	12.5041i	0.987509	+	0.570139i
$482$		0			0
$483$	13.0430	−	4.73541i	0.593477	−	0.215469i
$484$		0			0
$485$	36.8573	−	21.2796i	1.67360	−	0.966255i
$486$		0			0
$487$	16.8087	−	29.1136i	0.761677	−	1.31926i	−0.180309	−	0.983610i	$-0.557710\pi$
$487$	16.8087	−	29.1136i	0.761677	−	1.31926i	0.941986	−	0.335653i	$-0.108957\pi$
$488$		0			0
$489$	4.11408	+	2.80167i	0.186045	+	0.126696i
$490$		0			0
$491$	19.6893	−	11.3676i	0.888568	−	0.513015i	0.0150939	−	0.999886i	$-0.495195\pi$
$491$	19.6893	−	11.3676i	0.888568	−	0.513015i	0.873474	+	0.486871i	$0.161862\pi$
$492$		0			0
$493$	−31.1525	+	17.9859i	−1.40304	+	0.810043i
$494$		0			0
$495$	17.0251	+	13.5469i	0.765221	+	0.608886i
$496$		0			0
$497$	0.505884	+	1.12519i	0.0226920	+	0.0504716i
$498$		0			0
$499$	9.76175	−	16.9079i	0.436996	−	0.756899i	−0.560460	−	0.828181i	$-0.689376\pi$
$499$	9.76175	−	16.9079i	0.436996	−	0.756899i	0.997456	+	0.0712820i	$0.0227090\pi$
$500$		0			0
$501$	−2.09164	−	1.42440i	−0.0934477	−	0.0636373i
$502$		0			0
$503$	13.6867			0.610262			0.305131	−	0.952310i	$-0.401300\pi$
$503$	13.6867			0.610262			0.305131	+	0.952310i	$0.401300\pi$
$504$		0			0
$505$	46.6609			2.07638
$506$		0			0
$507$	−0.177389	+	2.38445i	−0.00787810	+	0.105897i
$508$		0			0
$509$	−1.14583	+	1.98464i	−0.0507881	+	0.0879675i	−0.890302	−	0.455371i	$-0.849507\pi$
$509$	−1.14583	+	1.98464i	−0.0507881	+	0.0879675i	0.839514	+	0.543338i	$0.182840\pi$
$510$		0			0
$511$	−11.0947	−	1.12527i	−0.490801	−	0.0497788i
$512$		0			0
$513$	1.55981	+	5.02772i	0.0688674	+	0.221979i
$514$		0			0
$515$	33.7226	−	19.4698i	1.48600	−	0.857940i
$516$		0			0
$517$	3.87018	−	2.23445i	0.170210	−	0.0982710i
$518$		0			0
$519$	−4.79082	+	2.31034i	−0.210294	+	0.101413i
$520$		0			0
$521$	8.54102	−	14.7935i	0.374189	−	0.648114i	−0.616017	−	0.787733i	$-0.711255\pi$
$521$	8.54102	−	14.7935i	0.374189	−	0.648114i	0.990205	+	0.139619i	$0.0445879\pi$
$522$		0			0
$523$	−35.7462	+	20.6381i	−1.56307	+	0.902440i	−0.566128	+	0.824317i	$0.691559\pi$
$523$	−35.7462	+	20.6381i	−1.56307	+	0.902440i	−0.996944	+	0.0781229i	$0.975107\pi$
$524$		0			0
$525$	−36.5473	−	6.47451i	−1.59505	−	0.282571i
$526$		0			0
$527$	4.86410	+	2.80829i	0.211883	+	0.122331i
$528$		0			0
$529$	−6.91563	−	11.9782i	−0.300679	−	0.520792i
$530$		0			0
$531$	−16.7857	+	21.0955i	−0.728435	+	0.915465i
$532$		0			0
$533$	−16.8294	−	9.71644i	−0.728961	−	0.420866i
$534$		0			0
$535$			9.55378i			0.413046i
$536$		0			0
$537$	−33.3698	−	2.48251i	−1.44001	−	0.107128i
$538$		0			0
$539$	2.81628	−	13.7409i	0.121306	−	0.591864i
$540$		0			0
$541$	22.7197	+	39.3516i	0.976795	+	1.69186i	0.673880	+	0.738841i	$0.264627\pi$
$541$	22.7197	+	39.3516i	0.976795	+	1.69186i	0.302915	+	0.953018i	$0.402040\pi$
$542$		0			0
$543$	5.93847	+	12.3143i	0.254844	+	0.528456i
$544$		0			0
$545$	16.3509	+	28.3206i	0.700395	+	1.21312i
$546$		0			0
$547$	−15.1095	+	26.1705i	−0.646037	+	1.11897i	0.338024	+	0.941138i	$0.390242\pi$
$547$	−15.1095	+	26.1705i	−0.646037	+	1.11897i	−0.984061	+	0.177832i	$0.943092\pi$
$548$		0			0
$549$	34.5369	+	27.4810i	1.47400	+	1.17286i
$550$		0			0
$551$	−5.90237			−0.251449
$552$		0			0
$553$	−9.23083	+	4.15018i	−0.392535	+	0.176484i
$554$		0			0
$555$	−41.4259	+	19.9774i	−1.75843	+	0.847992i
$556$		0			0
$557$	22.0154	+	12.7106i	0.932822	+	0.538565i	0.887703	−	0.460417i	$-0.152300\pi$
$557$	22.0154	+	12.7106i	0.932822	+	0.538565i	0.0451189	+	0.998982i	$0.485633\pi$
$558$		0			0
$559$		−	16.3585i		−	0.691892i
$560$		0			0
$561$	9.30799	+	19.3014i	0.392983	+	0.814907i
$562$		0			0
$563$	−2.88692			−0.121669			−0.0608346	−	0.998148i	$-0.519376\pi$
$563$	−2.88692			−0.121669			−0.0608346	+	0.998148i	$0.519376\pi$
$564$		0			0
$565$		−	6.11886i		−	0.257422i
$566$		0			0
$567$	−14.3933	−	18.9693i	−0.604462	−	0.796634i
$568$		0			0
$569$		−	44.5651i		−	1.86827i	−0.356922	−	0.934134i	$-0.616174\pi$
$569$		−	44.5651i		−	1.86827i	0.356922	−	0.934134i	$-0.383826\pi$
$570$		0			0
$571$	6.52939			0.273247			0.136623	−	0.990623i	$-0.456375\pi$
$571$	6.52939			0.273247			0.136623	+	0.990623i	$0.456375\pi$
$572$		0			0
$573$	−10.0095	−	20.7561i	−0.418153	−	0.867100i
$574$		0			0
$575$		−	24.5251i		−	1.02277i
$576$		0			0
$577$	1.17720	+	0.679658i	0.0490076	+	0.0282945i	0.524304	−	0.851531i	$-0.324326\pi$
$577$	1.17720	+	0.679658i	0.0490076	+	0.0282945i	−0.475296	+	0.879826i	$0.657659\pi$
$578$		0			0
$579$	10.1965	−	4.91719i	0.423752	−	0.204352i
$580$		0			0
$581$	2.13835	−	21.0833i	0.0887136	−	0.874683i
$582$		0			0
$583$	17.5405			0.726454
$584$		0			0
$585$	28.9621	+	23.0452i	1.19744	+	0.952800i
$586$		0			0
$587$	−22.2025	+	38.4559i	−0.916397	+	1.58725i	−0.111555	+	0.993758i	$0.535583\pi$
$587$	−22.2025	+	38.4559i	−0.916397	+	1.58725i	−0.804843	+	0.593488i	$0.797750\pi$
$588$		0			0
$589$	0.460793	+	0.798117i	0.0189866	+	0.0328858i
$590$		0			0
$591$	3.34234	+	6.93082i	0.137485	+	0.285096i
$592$		0			0
$593$	7.17564	+	12.4286i	0.294668	+	0.510380i	0.974908	−	0.222610i	$-0.0714576\pi$
$593$	7.17564	+	12.4286i	0.294668	+	0.510380i	−0.680240	+	0.732990i	$0.738124\pi$
$594$		0			0
$595$	−47.9576	−	34.5771i	−1.96607	−	1.41752i
$596$		0			0
$597$	−19.8824	−	1.47913i	−0.813733	−	0.0605368i
$598$		0			0
$599$		−	3.50277i		−	0.143119i	−0.997436	−	0.0715597i	$-0.977202\pi$
$599$		−	3.50277i		−	0.143119i	0.997436	−	0.0715597i	$-0.0227977\pi$
$600$		0			0
$601$	15.1846	+	8.76685i	0.619394	+	0.357607i	0.776633	−	0.629953i	$-0.216926\pi$
$601$	15.1846	+	8.76685i	0.619394	+	0.357607i	−0.157239	+	0.987561i	$0.550259\pi$
$602$		0			0
$603$	15.5344	−	19.5230i	0.632610	−	0.795037i
$604$		0			0
$605$	−12.6401	−	21.8933i	−0.513894	−	0.890090i
$606$		0			0
$607$	−0.0755923	−	0.0436432i	−0.00306820	−	0.00177142i	0.498465	−	0.866910i	$-0.333897\pi$
$607$	−0.0755923	−	0.0436432i	−0.00306820	−	0.00177142i	−0.501533	+	0.865138i	$0.667231\pi$
$608$		0			0
$609$	25.0960	−	9.11140i	1.01694	−	0.369213i
$610$		0			0
$611$	6.58373	−	3.80112i	0.266349	−	0.153777i
$612$		0			0
$613$	12.5352	−	21.7116i	0.506292	−	0.876924i	−0.493681	−	0.869643i	$-0.664349\pi$
$613$	12.5352	−	21.7116i	0.506292	−	0.876924i	0.999973	−	0.00728071i	$-0.00231754\pi$
$614$		0			0
$615$	32.1904	−	15.5236i	1.29804	−	0.625972i
$616$		0			0
$617$	−10.6365	+	6.14101i	−0.428211	+	0.247228i	−0.698584	−	0.715528i	$-0.746186\pi$
$617$	−10.6365	+	6.14101i	−0.428211	+	0.247228i	0.270373	+	0.962756i	$0.412853\pi$
$618$		0			0
$619$	17.5869	−	10.1538i	0.706875	−	0.408115i	−0.103028	−	0.994678i	$-0.532853\pi$
$619$	17.5869	−	10.1538i	0.706875	−	0.408115i	0.809903	+	0.586564i	$0.199520\pi$
$620$		0			0
$621$	10.6830	−	11.5512i	0.428694	−	0.463533i
$622$		0			0
$623$	−10.2723	−	7.40625i	−0.411550	−	0.296725i
$624$		0			0
$625$	−0.0518970	+	0.0898882i	−0.00207588	+	0.00359553i
$626$		0			0
$627$	−0.260854	+	3.50638i	−0.0104175	+	0.140031i
$628$		0			0
$629$	−45.2969			−1.80610
$630$		0			0
$631$	45.9665			1.82990			0.914950	−	0.403568i	$-0.132230\pi$
$631$	45.9665			1.82990			0.914950	+	0.403568i	$0.132230\pi$
$632$		0			0
$633$	−32.3561	−	22.0343i	−1.28604	−	0.875784i
$634$		0			0
$635$	32.4456	−	56.1975i	1.28757	−	2.23013i
$636$		0			0
$637$	4.79090	−	23.3753i	0.189822	−	0.926163i
$638$		0			0
$639$	1.09462	+	0.870989i	0.0433025	+	0.0344558i
$640$		0			0
$641$	−27.4104	+	15.8254i	−1.08265	+	0.625067i	−0.931609	−	0.363461i	$-0.881595\pi$
$641$	−27.4104	+	15.8254i	−1.08265	+	0.625067i	−0.151038	+	0.988528i	$0.548262\pi$
$642$		0			0
$643$	10.0106	−	5.77960i	0.394778	−	0.227925i	−0.289450	−	0.957193i	$-0.593472\pi$
$643$	10.0106	−	5.77960i	0.394778	−	0.227925i	0.684228	+	0.729268i	$0.260139\pi$
$644$		0			0
$645$	24.8658	+	16.9335i	0.979091	+	0.666755i
$646$		0			0
$647$	13.0365	−	22.5799i	0.512519	−	0.887708i	−0.487376	−	0.873192i	$-0.662046\pi$
$647$	13.0365	−	22.5799i	0.512519	−	0.887708i	0.999895	−	0.0145160i	$-0.00462076\pi$
$648$		0			0
$649$	−15.5942	+	9.00332i	−0.612126	+	0.353411i
$650$		0			0
$651$	−3.19127	−	2.68216i	−0.125076	−	0.105122i
$652$		0			0
$653$	16.3952	+	9.46576i	0.641593	+	0.370424i	0.785228	−	0.619207i	$-0.212546\pi$
$653$	16.3952	+	9.46576i	0.641593	+	0.370424i	−0.143635	+	0.989631i	$0.545879\pi$
$654$		0			0
$655$	−31.3638	−	54.3237i	−1.22549	−	2.12260i
$656$		0			0
$657$	−11.7656	+	4.63242i	−0.459021	+	0.180728i
$658$		0			0
$659$	−23.3508	−	13.4816i	−0.909618	−	0.525168i	−0.0293098	−	0.999570i	$-0.509331\pi$
$659$	−23.3508	−	13.4816i	−0.909618	−	0.525168i	−0.880308	+	0.474402i	$0.842664\pi$
$660$		0			0
$661$			25.7730i			1.00245i	0.865316	+	0.501227i	$0.167118\pi$
$661$			25.7730i			1.00245i	−0.865316	+	0.501227i	$0.832882\pi$
$662$		0			0
$663$	15.8342	+	32.8345i	0.614950	+	1.27519i
$664$		0			0
$665$	−3.97803	−	8.84793i	−0.154261	−	0.343108i
$666$		0			0
$667$	8.82079	+	15.2780i	0.341542	+	0.591568i
$668$		0			0
$669$	−32.5089	−	2.41847i	−1.25687	−	0.0935034i
$670$		0			0
$671$	14.7400	+	25.5304i	0.569030	+	0.985590i
$672$		0			0
$673$	−12.9608	+	22.4487i	−0.499601	+	0.865335i	−1.00000		0.000460130i	$-0.999854\pi$
$673$	−12.9608	+	22.4487i	−0.499601	+	0.865335i	0.500398	+	0.865795i	$0.333187\pi$
$674$		0			0
$675$	−40.1959	+	12.4705i	−1.54714	+	0.479990i
$676$		0			0
$677$	13.1076			0.503767			0.251884	−	0.967758i	$-0.418950\pi$
$677$	13.1076			0.503767			0.251884	+	0.967758i	$0.418950\pi$
$678$		0			0
$679$	−30.9523	−	3.13930i	−1.18784	−	0.120475i
$680$		0			0
$681$	20.9207	+	14.2468i	0.801681	+	0.545940i
$682$		0			0
$683$	−25.6910	−	14.8327i	−0.983038	−	0.567557i	−0.0798523	−	0.996807i	$-0.525445\pi$
$683$	−25.6910	−	14.8327i	−0.983038	−	0.567557i	−0.903186	+	0.429249i	$0.858778\pi$
$684$		0			0
$685$			0.00233490i			8.92121e-5i
$686$		0			0
$687$	4.10952	+	0.305723i	0.156788	+	0.0116641i
$688$		0			0
$689$	29.8390			1.13677
$690$		0			0
$691$			47.3159i			1.79998i	0.435910	+	0.899990i	$0.356427\pi$
$691$			47.3159i			1.79998i	−0.435910	+	0.899990i	$0.643573\pi$
$692$		0			0
$693$	−4.30364	−	15.3113i	−0.163482	−	0.581628i
$694$		0			0
$695$			36.4961i			1.38437i
$696$		0			0
$697$	35.1983			1.33323
$698$		0			0
$699$	10.1708	−	14.9352i	0.384693	−	0.564900i
$700$		0			0
$701$		−	13.7742i		−	0.520244i	−0.965576	−	0.260122i	$-0.916237\pi$
$701$		−	13.7742i		−	0.520244i	0.965576	−	0.260122i	$-0.0837627\pi$
$702$		0			0
$703$	−6.43670	−	3.71623i	−0.242765	−	0.140160i
$704$		0			0
$705$	−1.03723	+	13.9423i	−0.0390642	+	0.525099i
$706$		0			0
$707$	−27.6680	−	19.9485i	−1.04056	−	0.750239i
$708$		0			0
$709$	−43.9383			−1.65014			−0.825069	−	0.565032i	$-0.808864\pi$
$709$	−43.9383			−1.65014			−0.825069	+	0.565032i	$0.808864\pi$
$710$		0			0
$711$	−7.14543	+	8.98006i	−0.267975	+	0.336779i
$712$		0			0
$713$	1.37726	−	2.38549i	0.0515789	−	0.0893373i
$714$		0			0
$715$	12.3607	+	21.4094i	0.462265	+	0.800667i
$716$		0			0
$717$	−23.1871	+	34.0488i	−0.865936	+	1.27158i
$718$		0			0
$719$	14.7930	+	25.6223i	0.551687	+	0.955549i	0.998153	+	0.0607489i	$0.0193489\pi$
$719$	14.7930	+	25.6223i	0.551687	+	0.955549i	−0.446466	+	0.894800i	$0.647318\pi$
$720$		0			0
$721$	−28.3198	−	2.87230i	−1.05469	−	0.106970i
$722$		0			0
$723$	27.9303	−	41.0140i	1.03874	−	1.52533i
$724$		0			0
$725$		−	47.1887i		−	1.75254i
$726$		0			0
$727$	−10.1244	−	5.84534i	−0.375494	−	0.216792i	0.300362	−	0.953825i	$-0.402893\pi$
$727$	−10.1244	−	5.84534i	−0.375494	−	0.216792i	−0.675856	+	0.737034i	$0.736226\pi$
$728$		0			0
$729$	−24.3642	−	11.6356i	−0.902377	−	0.430948i
$730$		0			0
$731$	14.8149	+	25.6602i	0.547949	+	0.949076i
$732$		0			0
$733$	−28.6423	−	16.5366i	−1.05793	−	0.610795i	−0.133070	−	0.991107i	$-0.542483\pi$
$733$	−28.6423	−	16.5366i	−1.05793	−	0.610795i	−0.924858	+	0.380312i	$0.875817\pi$
$734$		0			0
$735$	30.5724	+	31.4793i	1.12768	+	1.16113i
$736$		0			0
$737$	14.4318	−	8.33219i	0.531601	−	0.306920i
$738$		0			0
$739$	21.7528	−	37.6770i	0.800190	−	1.38597i	−0.119301	−	0.992858i	$-0.538065\pi$
$739$	21.7528	−	37.6770i	0.800190	−	1.38597i	0.919491	−	0.393111i	$-0.128601\pi$
$740$		0			0
$741$	−0.443750	+	5.96486i	−0.0163016	+	0.219125i
$742$		0			0
$743$	−18.0206	+	10.4042i	−0.661112	+	0.381693i	−0.792701	−	0.609611i	$-0.791326\pi$
$743$	−18.0206	+	10.4042i	−0.661112	+	0.381693i	0.131589	+	0.991304i	$0.457992\pi$
$744$		0			0
$745$	35.2544	−	20.3542i	1.29162	−	0.745719i
$746$		0			0
$747$	−8.80300	−	22.3583i	−0.322085	−	0.818048i
$748$		0			0
$749$	4.08443	−	5.66501i	0.149242	−	0.206995i
$750$		0			0
$751$	−19.9492	+	34.5531i	−0.727957	+	1.26086i	0.229788	+	0.973241i	$0.426197\pi$
$751$	−19.9492	+	34.5531i	−0.727957	+	1.26086i	−0.957745	+	0.287618i	$0.907137\pi$
$752$		0			0
$753$	17.2083	−	8.29858i	0.627105	−	0.302417i
$754$		0			0
$755$	17.0969			0.622219
$756$		0			0
$757$	7.45545			0.270973			0.135486	−	0.990779i	$-0.456740\pi$
$757$	7.45545			0.270973			0.135486	+	0.990779i	$0.456740\pi$
$758$		0			0
$759$	9.46597	−	4.56490i	0.343593	−	0.165695i
$760$		0			0
$761$	−4.32462	+	7.49046i	−0.156767	+	0.271529i	−0.933701	−	0.358053i	$-0.883441\pi$
$761$	−4.32462	+	7.49046i	−0.156767	+	0.271529i	0.776934	+	0.629582i	$0.216774\pi$
$762$		0			0
$763$	2.41219	−	23.7833i	0.0873271	−	0.861013i
$764$		0			0
$765$	−66.3010	−	9.91969i	−2.39712	−	0.358647i
$766$		0			0
$767$	−26.5280	+	15.3159i	−0.957870	+	0.553026i
$768$		0			0
$769$	20.4818	−	11.8252i	0.738592	−	0.426426i	−0.0829652	−	0.996552i	$-0.526439\pi$
$769$	20.4818	−	11.8252i	0.738592	−	0.426426i	0.821557	+	0.570126i	$0.193106\pi$
$770$		0			0
$771$	−1.94005	+	26.0781i	−0.0698693	+	0.939180i
$772$		0			0
$773$	23.2849	−	40.3307i	0.837501	−	1.45059i	−0.0544774	−	0.998515i	$-0.517349\pi$
$773$	23.2849	−	40.3307i	0.837501	−	1.45059i	0.891978	−	0.452079i	$-0.149317\pi$
$774$		0			0
$775$	−6.38084	+	3.68398i	−0.229207	+	0.132333i
$776$		0			0
$777$	33.1046	+	5.86462i	1.18762	+	0.210392i
$778$		0			0
$779$	5.00170	+	2.88773i	0.179204	+	0.103464i
$780$		0			0
$781$	0.467172	+	0.809166i	0.0167167	+	0.0289542i
$782$		0			0
$783$	20.5551	−	22.2256i	0.734580	−	0.794279i
$784$		0			0
$785$	−9.62178	−	5.55513i	−0.343416	−	0.198271i
$786$		0			0
$787$			24.4400i			0.871192i	0.900142	+	0.435596i	$0.143462\pi$
$787$			24.4400i			0.871192i	−0.900142	+	0.435596i	$0.856538\pi$
$788$		0			0
$789$	−19.1460	+	28.1148i	−0.681617	+	1.00091i
$790$		0			0
$791$	−2.61593	+	3.62823i	−0.0930118	+	0.129005i
$792$		0			0
$793$	25.0748	+	43.4309i	0.890433	+	1.54228i
$794$		0			0
$795$	−30.8877	+	45.3568i	−1.09547	+	1.60864i
$796$		0			0
$797$	−24.9202	−	43.1631i	−0.882719	−	1.52891i	−0.848306	−	0.529506i	$-0.822377\pi$
$797$	−24.9202	−	43.1631i	−0.882719	−	1.52891i	−0.0344128	−	0.999408i	$-0.510956\pi$
$798$		0			0
$799$	−6.88489	+	11.9250i	−0.243570	+	0.421875i
$800$		0			0
$801$	−14.2014	−	2.12475i	−0.501780	−	0.0750743i
$802$		0			0
$803$	−8.44583			−0.298047
$804$		0			0
$805$	−16.9576	+	23.5198i	−0.597676	+	0.828963i
$806$		0			0
$807$	0.0630937	−	0.848103i	0.00222100	−	0.0298546i
$808$		0			0
$809$	−10.6735	−	6.16237i	−0.375262	−	0.216657i	0.300493	−	0.953784i	$-0.402849\pi$
$809$	−10.6735	−	6.16237i	−0.375262	−	0.216657i	−0.675755	+	0.737127i	$0.736182\pi$
$810$		0			0
$811$			24.8017i			0.870906i	0.900212	+	0.435453i	$0.143412\pi$
$811$			24.8017i			0.870906i	−0.900212	+	0.435453i	$0.856588\pi$
$812$		0			0
$813$	13.7258	−	20.1556i	0.481386	−	0.706888i
$814$		0			0
$815$	−10.4009			−0.364329
$816$		0			0
$817$			4.86176i			0.170091i
$818$		0			0
$819$	−7.32111	−	26.0467i	−0.255820	−	0.910146i
$820$		0			0
$821$			36.2083i			1.26368i	0.775100	+	0.631839i	$0.217700\pi$
$821$			36.2083i			1.26368i	−0.775100	+	0.631839i	$0.782300\pi$
$822$		0			0
$823$	19.0819			0.665152			0.332576	−	0.943076i	$-0.392082\pi$
$823$	19.0819			0.665152			0.332576	+	0.943076i	$0.392082\pi$
$824$		0			0
$825$	−28.0331	−	2.08549i	−0.975986	−	0.0726075i
$826$		0			0
$827$			31.9013i			1.10932i	0.832079	+	0.554658i	$0.187151\pi$
$827$			31.9013i			1.10932i	−0.832079	+	0.554658i	$0.812849\pi$
$828$		0			0
$829$	13.0645	+	7.54278i	0.453748	+	0.261971i	0.709412	−	0.704794i	$-0.248961\pi$
$829$	13.0645	+	7.54278i	0.453748	+	0.261971i	−0.255664	+	0.966766i	$0.582294\pi$
$830$		0			0
$831$	−43.9793	−	29.9497i	−1.52563	−	1.03894i
$832$		0			0
$833$	13.6545	+	41.0056i	0.473101	+	1.42076i
$834$		0			0
$835$	5.28795			0.182997
$836$		0			0
$837$	−4.61007	−	1.04432i	−0.159347	−	0.0360972i
$838$		0			0
$839$	8.19860	−	14.2004i	0.283047	−	0.490252i	−0.689087	−	0.724679i	$-0.741988\pi$
$839$	8.19860	−	14.2004i	0.283047	−	0.490252i	0.972134	+	0.234427i	$0.0753214\pi$
$840$		0			0
$841$	2.47206	+	4.28173i	0.0852434	+	0.147646i
$842$		0			0
$843$	13.6879	+	1.01830i	0.471436	+	0.0350720i
$844$		0			0
$845$	−2.49817	−	4.32696i	−0.0859397	−	0.148852i
$846$		0			0
$847$	−1.86475	+	18.3857i	−0.0640735	+	0.631741i
$848$		0			0
$849$	8.66402	+	17.9661i	0.297348	+	0.616594i
$850$		0			0
$851$			22.2149i			0.761516i
$852$		0			0
$853$	16.5936	+	9.58030i	0.568153	+	0.328023i	0.756411	−	0.654096i	$-0.226951\pi$
$853$	16.5936	+	9.58030i	0.568153	+	0.328023i	−0.188258	+	0.982120i	$0.560284\pi$
$854$		0			0
$855$	−8.60756	−	6.84903i	−0.294372	−	0.234232i
$856$		0			0
$857$	8.05723	+	13.9555i	0.275230	+	0.476712i	0.970193	−	0.242333i	$-0.0779127\pi$
$857$	8.05723	+	13.9555i	0.275230	+	0.476712i	−0.694963	+	0.719045i	$0.744579\pi$
$858$		0			0
$859$	−10.4830	−	6.05238i	−0.357677	−	0.206505i	0.310384	−	0.950611i	$-0.399542\pi$
$859$	−10.4830	−	6.05238i	−0.357677	−	0.206505i	−0.668061	+	0.744106i	$0.732876\pi$
$860$		0			0
$861$	−25.7242	−	4.55716i	−0.876679	−	0.155308i
$862$		0			0
$863$	−32.2728	+	18.6327i	−1.09858	+	0.634265i	−0.935848	−	0.352405i	$-0.885364\pi$
$863$	−32.2728	+	18.6327i	−1.09858	+	0.634265i	−0.162732	+	0.986670i	$0.552031\pi$
$864$		0			0
$865$	5.55712	−	9.62522i	0.188948	−	0.327267i
$866$		0			0
$867$	−30.2365	−	20.5909i	−1.02689	−	0.699303i
$868$		0			0
$869$	−6.63824	+	3.83259i	−0.225187	+	0.130012i
$870$		0			0
$871$	24.5505	−	14.1743i	0.831863	−	0.480276i
$872$		0			0
$873$	−32.8241	+	12.9236i	−1.11093	+	0.437399i
$874$		0			0
$875$	27.0696	−	12.1705i	0.915120	−	0.411437i
$876$		0			0
$877$	4.85474	−	8.40866i	0.163933	−	0.283940i	−0.772343	−	0.635206i	$-0.780915\pi$
$877$	4.85474	−	8.40866i	0.163933	−	0.283940i	0.936276	+	0.351266i	$0.114249\pi$
$878$		0			0
$879$	−7.18493	−	4.89289i	−0.242342	−	0.165033i
$880$		0			0
$881$	−2.63241			−0.0886881			−0.0443440	−	0.999016i	$-0.514120\pi$
$881$	−2.63241			−0.0886881			−0.0443440	+	0.999016i	$0.514120\pi$
$882$		0			0
$883$	36.3181			1.22220			0.611101	−	0.791553i	$-0.290727\pi$
$883$	36.3181			1.22220			0.611101	+	0.791553i	$0.290727\pi$
$884$		0			0
$885$	4.17932	−	56.1782i	0.140486	−	1.88841i
$886$		0			0
$887$	8.18209	−	14.1718i	0.274728	−	0.475842i	−0.695339	−	0.718682i	$-0.744746\pi$
$887$	8.18209	−	14.1718i	0.274728	−	0.475842i	0.970066	+	0.242840i	$0.0780790\pi$
$888$		0			0
$889$	−43.2645	+	19.4517i	−1.45104	+	0.652389i
$890$		0			0
$891$	−12.2950	−	13.1933i	−0.411898	−	0.441993i
$892$		0			0
$893$	−1.95669	+	1.12969i	−0.0654781	+	0.0378038i
$894$		0			0
$895$	60.5549	−	34.9614i	2.02413	−	1.16863i
$896$		0			0
$897$	16.1030	−	7.76555i	0.537663	−	0.259284i
$898$		0			0
$899$	2.64999	−	4.58992i	0.0883822	−	0.153082i
$900$		0			0
$901$	−46.8058	+	27.0233i	−1.55933	+	0.900277i
$902$		0			0
$903$	−7.50503	−	20.6715i	−0.249752	−	0.687904i
$904$		0			0
$905$	−24.7405	−	14.2839i	−0.822403	−	0.474814i
$906$		0			0
$907$	5.41666	+	9.38192i	0.179857	+	0.311522i	0.941831	−	0.336086i	$-0.109103\pi$
$907$	5.41666	+	9.38192i	0.179857	+	0.311522i	−0.761974	+	0.647607i	$0.775770\pi$
$908$		0			0
$909$	−38.2509	−	5.72294i	−1.26870	−	0.189818i
$910$		0			0
$911$	−36.8512	−	21.2760i	−1.22093	−	0.704907i	−0.255817	−	0.966725i	$-0.582345\pi$
$911$	−36.8512	−	21.2760i	−1.22093	−	0.704907i	−0.965117	+	0.261818i	$0.915678\pi$
$912$		0			0
$913$		−	16.0496i		−	0.531166i
$914$		0			0
$915$	−91.9734	−	6.84227i	−3.04055	−	0.226198i
$916$		0			0
$917$	−4.62699	+	45.6204i	−0.152797	+	1.50652i
$918$		0			0
$919$	12.9697	+	22.4641i	0.427829	+	0.741022i	0.996680	−	0.0814187i	$-0.0259451\pi$
$919$	12.9697	+	22.4641i	0.427829	+	0.741022i	−0.568851	+	0.822441i	$0.692612\pi$
$920$		0			0
$921$	13.1895	+	27.3502i	0.434608	+	0.901221i
$922$		0			0
$923$	0.794727	+	1.37651i	0.0261588	+	0.0453083i
$924$		0			0
$925$	29.7108	−	51.4606i	0.976884	−	1.69201i
$926$		0			0
$927$	−30.0324	+	11.8245i	−0.986395	+	0.388367i
$928$		0			0
$929$	46.8911			1.53845			0.769224	−	0.638979i	$-0.220643\pi$
$929$	46.8911			1.53845			0.769224	+	0.638979i	$0.220643\pi$
$930$		0			0
$931$	−1.42386	+	6.94715i	−0.0466650	+	0.227684i
$932$		0			0
$933$	−26.9825	+	13.0121i	−0.883367	+	0.425998i
$934$		0			0
$935$	−38.7784	−	22.3887i	−1.26819	−	0.732189i
$936$		0			0
$937$		−	0.209357i		−	0.00683939i	−0.999994	−	0.00341969i	$-0.998911\pi$
$937$		−	0.209357i		−	0.00683939i	0.999994	−	0.00341969i	$-0.00108852\pi$
$938$		0			0
$939$	−6.76742	−	14.0332i	−0.220846	−	0.457956i
$940$		0			0
$941$	−0.777130			−0.0253337			−0.0126669	−	0.999920i	$-0.504032\pi$
$941$	−0.777130			−0.0253337			−0.0126669	+	0.999920i	$0.504032\pi$
$942$		0			0
$943$		−	17.2623i		−	0.562137i
$944$		0			0
$945$	47.1708	+	15.8337i	1.53447	+	0.515071i
$946$		0			0
$947$		−	49.7945i		−	1.61810i	−0.587737	−	0.809052i	$-0.699981\pi$
$947$		−	49.7945i		−	1.61810i	0.587737	−	0.809052i	$-0.300019\pi$
$948$		0			0
$949$	−14.3676			−0.466391
$950$		0			0
$951$	−5.05612	−	10.4846i	−0.163956	−	0.339986i
$952$		0			0
$953$		−	41.4104i		−	1.34141i	−0.741722	−	0.670707i	$-0.765991\pi$
$953$		−	41.4104i		−	1.34141i	0.741722	−	0.670707i	$-0.234009\pi$
$954$		0			0
$955$	41.7010	+	24.0761i	1.34941	+	0.779084i
$956$		0			0
$957$	18.2135	−	8.78332i	0.588757	−	0.283924i
$958$		0			0
$959$	0.000998217	−	0.00138450i	3.22341e−5	−	4.47079e-5i
$960$		0			0
$961$	30.1725			0.973305
$962$		0			0
$963$	1.17177	−	7.83183i	0.0377596	−	0.252377i
$964$		0			0
$965$	−11.8274	+	20.4857i	−0.380739	+	0.659459i
$966$		0			0
$967$	−22.8028	−	39.4956i	−0.733289	−	1.27009i	−0.955470	−	0.295088i	$-0.904651\pi$
$967$	−22.8028	−	39.4956i	−0.733289	−	1.27009i	0.222181	−	0.975005i	$-0.428682\pi$
$968$		0			0
$969$	−4.70594	−	9.75843i	−0.151177	−	0.313486i
$970$		0			0
$971$	4.36733	+	7.56444i	0.140154	+	0.242754i	0.927555	−	0.373688i	$-0.121907\pi$
$971$	4.36733	+	7.56444i	0.140154	+	0.242754i	−0.787400	+	0.616442i	$0.788573\pi$
$972$		0			0
$973$	15.6028	−	21.6407i	0.500202	−	0.693768i
$974$		0			0
$975$	−47.6883	−	3.54772i	−1.52725	−	0.113618i
$976$		0			0
$977$			14.9023i			0.476766i	0.971171	+	0.238383i	$0.0766174\pi$
$977$			14.9023i			0.476766i	−0.971171	+	0.238383i	$0.923383\pi$
$978$		0			0
$979$	−8.30615	−	4.79556i	−0.265466	−	0.153267i
$980$		0			0
$981$	−9.93033	−	25.2216i	−0.317051	−	0.805262i
$982$		0			0
$983$	1.53458	+	2.65798i	0.0489456	+	0.0847763i	0.889460	−	0.457013i	$-0.151081\pi$
$983$	1.53458	+	2.65798i	0.0489456	+	0.0847763i	−0.840515	+	0.541789i	$0.817747\pi$
$984$		0			0
$985$	−13.9247	−	8.03941i	−0.443677	−	0.256157i
$986$		0			0
$987$	6.57566	−	7.82381i	0.209306	−	0.249035i
$988$		0			0
$989$	12.5845	−	7.26565i	0.400163	−	0.231034i
$990$		0			0
$991$	−27.9075	+	48.3372i	−0.886510	+	1.53548i	−0.0425375	+	0.999095i	$0.513544\pi$
$991$	−27.9075	+	48.3372i	−0.886510	+	1.53548i	−0.843973	+	0.536386i	$0.819789\pi$
$992$		0			0
$993$	29.2904	−	14.1251i	0.929502	−	0.448246i
$994$		0			0
$995$	36.0798	−	20.8307i	1.14381	−	0.660377i
$996$		0			0
$997$	5.30607	−	3.06346i	0.168045	−	0.0970208i	−0.413619	−	0.910450i	$-0.635735\pi$
$997$	5.30607	−	3.06346i	0.168045	−	0.0970208i	0.581664	+	0.813429i	$0.302402\pi$
$998$		0			0
$999$	36.4096	−	11.2958i	1.15195	−	0.357384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.ca.c.353.8		16
3.2	odd	2		3024.2.ca.c.2033.7		16
4.3	odd	2		126.2.l.a.101.1	yes	16
7.5	odd	6		1008.2.df.c.929.5		16
9.4	even	3		3024.2.df.c.17.7		16
9.5	odd	6		1008.2.df.c.689.5		16
12.11	even	2		378.2.l.a.143.8		16
21.5	even	6		3024.2.df.c.1601.7		16
28.3	even	6		882.2.m.a.587.6		16
28.11	odd	6		882.2.m.b.587.7		16
28.19	even	6		126.2.t.a.47.2	yes	16
28.23	odd	6		882.2.t.a.803.3		16
28.27	even	2		882.2.l.b.227.4		16
36.7	odd	6		1134.2.k.a.647.1		16
36.11	even	6		1134.2.k.b.647.8		16
36.23	even	6		126.2.t.a.59.2	yes	16
36.31	odd	6		378.2.t.a.17.8		16
63.5	even	6	inner	1008.2.ca.c.257.8		16
63.40	odd	6		3024.2.ca.c.2609.7		16
84.11	even	6		2646.2.m.b.1763.4		16
84.23	even	6		2646.2.t.b.1979.5		16
84.47	odd	6		378.2.t.a.89.8		16
84.59	odd	6		2646.2.m.a.1763.1		16
84.83	odd	2		2646.2.l.a.521.5		16
252.23	even	6		882.2.l.b.509.8		16
252.31	even	6		2646.2.m.b.881.4		16
252.47	odd	6		1134.2.k.a.971.1		16
252.59	odd	6		882.2.m.b.293.7		16
252.67	odd	6		2646.2.m.a.881.1		16
252.95	even	6		882.2.m.a.293.6		16
252.103	even	6		378.2.l.a.341.4		16
252.131	odd	6		126.2.l.a.5.5	✓	16
252.139	even	6		2646.2.t.b.2285.5		16
252.167	odd	6		882.2.t.a.815.3		16
252.187	even	6		1134.2.k.b.971.8		16
252.247	odd	6		2646.2.l.a.1097.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.5	✓	16	252.131	odd	6
126.2.l.a.101.1	yes	16	4.3	odd	2
126.2.t.a.47.2	yes	16	28.19	even	6
126.2.t.a.59.2	yes	16	36.23	even	6
378.2.l.a.143.8		16	12.11	even	2
378.2.l.a.341.4		16	252.103	even	6
378.2.t.a.17.8		16	36.31	odd	6
378.2.t.a.89.8		16	84.47	odd	6
882.2.l.b.227.4		16	28.27	even	2
882.2.l.b.509.8		16	252.23	even	6
882.2.m.a.293.6		16	252.95	even	6
882.2.m.a.587.6		16	28.3	even	6
882.2.m.b.293.7		16	252.59	odd	6
882.2.m.b.587.7		16	28.11	odd	6
882.2.t.a.803.3		16	28.23	odd	6
882.2.t.a.815.3		16	252.167	odd	6
1008.2.ca.c.257.8		16	63.5	even	6	inner
1008.2.ca.c.353.8		16	1.1	even	1	trivial
1008.2.df.c.689.5		16	9.5	odd	6
1008.2.df.c.929.5		16	7.5	odd	6
1134.2.k.a.647.1		16	36.7	odd	6
1134.2.k.a.971.1		16	252.47	odd	6
1134.2.k.b.647.8		16	36.11	even	6
1134.2.k.b.971.8		16	252.187	even	6
2646.2.l.a.521.5		16	84.83	odd	2
2646.2.l.a.1097.1		16	252.247	odd	6
2646.2.m.a.881.1		16	252.67	odd	6
2646.2.m.a.1763.1		16	84.59	odd	6
2646.2.m.b.881.4		16	252.31	even	6
2646.2.m.b.1763.4		16	84.11	even	6
2646.2.t.b.1979.5		16	84.23	even	6
2646.2.t.b.2285.5		16	252.139	even	6
3024.2.ca.c.2033.7		16	3.2	odd	2
3024.2.ca.c.2609.7		16	63.40	odd	6
3024.2.df.c.17.7		16	9.4	even	3
3024.2.df.c.1601.7		16	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.56012 - 0.752355i) q^{3} +(-1.80966 + 3.13442i) q^{5} +(2.41308 - 1.08492i) q^{7} +(1.86792 - 2.34752i) q^{9} +O(q^{10})\)	\(q+(1.56012 - 0.752355i) q^{3} +(-1.80966 + 3.13442i) q^{5} +(2.41308 - 1.08492i) q^{7} +(1.86792 - 2.34752i) q^{9} +(1.73534 - 1.00190i) q^{11} +(2.95206 - 1.70437i) q^{13} +(-0.465079 + 6.25156i) q^{15} +(-3.08709 + 5.34700i) q^{17} +(-0.877353 + 0.506540i) q^{19} +(2.94844 - 3.50809i) q^{21} +(2.62232 + 1.51400i) q^{23} +(-4.04972 - 7.01433i) q^{25} +(1.14800 - 5.06775i) q^{27} +(5.04560 + 2.91308i) q^{29} -0.909687i q^{31} +(1.95354 - 2.86867i) q^{33} +(-0.966257 + 9.52693i) q^{35} +(3.66825 + 6.35359i) q^{37} +(3.32326 - 4.88001i) q^{39} +(-2.85045 - 4.93712i) q^{41} +(2.39949 - 4.15605i) q^{43} +(3.97782 + 10.1031i) q^{45} +2.23022 q^{47} +(4.64590 - 5.23599i) q^{49} +(-0.793376 + 10.6645i) q^{51} +(7.58088 + 4.37683i) q^{53} +7.25237i q^{55} +(-0.987674 + 1.45034i) q^{57} -8.98627 q^{59} +14.7121i q^{61} +(1.96057 - 7.69130i) q^{63} +12.3373i q^{65} +8.31641 q^{67} +(5.23019 + 0.389094i) q^{69} +0.466287i q^{71} +(-3.65022 - 2.10746i) q^{73} +(-11.5953 - 7.89633i) q^{75} +(3.10053 - 4.30036i) q^{77} -3.82533 q^{79} +(-2.02173 - 8.76998i) q^{81} +(4.00481 - 6.93654i) q^{83} +(-11.1732 - 19.3525i) q^{85} +(10.0634 + 0.748656i) q^{87} +(-2.39324 - 4.14521i) q^{89} +(5.27445 - 7.31553i) q^{91} +(-0.684408 - 1.41922i) q^{93} -3.66666i q^{95} +(-10.1835 - 5.87944i) q^{97} +(0.889499 - 5.94521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7}+O(q^{10}) \) 16 * q - 2 * q^7	\( 16 q - 2 q^{7} - 12 q^{11} + 6 q^{13} + 18 q^{15} - 18 q^{17} - 12 q^{21} + 6 q^{23} - 8 q^{25} - 36 q^{27} + 6 q^{29} - 30 q^{35} - 2 q^{37} + 12 q^{39} - 6 q^{41} + 2 q^{43} - 30 q^{45} + 36 q^{47} - 8 q^{49} - 6 q^{51} - 36 q^{53} + 6 q^{57} - 60 q^{59} - 36 q^{63} + 28 q^{67} - 42 q^{69} - 60 q^{75} - 42 q^{77} - 32 q^{79} - 36 q^{81} - 12 q^{85} + 24 q^{87} - 24 q^{89} + 12 q^{91} - 42 q^{93} + 6 q^{97} - 18 q^{99}+O(q^{100}) \) 16 * q - 2 * q^7 - 12 * q^11 + 6 * q^13 + 18 * q^15 - 18 * q^17 - 12 * q^21 + 6 * q^23 - 8 * q^25 - 36 * q^27 + 6 * q^29 - 30 * q^35 - 2 * q^37 + 12 * q^39 - 6 * q^41 + 2 * q^43 - 30 * q^45 + 36 * q^47 - 8 * q^49 - 6 * q^51 - 36 * q^53 + 6 * q^57 - 60 * q^59 - 36 * q^63 + 28 * q^67 - 42 * q^69 - 60 * q^75 - 42 * q^77 - 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^87 - 24 * q^89 + 12 * q^91 - 42 * q^93 + 6 * q^97 - 18 * q^99

Introduction

L-functions

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